# Triangle calculator

Please enter what you know about the triangle:
You have entered side a, b and angle β.

Triangle has two solutions: a=38.5; b=34.5; c=5.14552145419 and a=38.5; b=34.5; c=56.75217637256.

### #1 Obtuse scalene triangle.

Sides: a = 38.5   b = 34.5   c = 5.14552145419

Area: T = 58.91444489058
Perimeter: p = 78.14552145419
Semiperimeter: s = 39.0732607271

Angle ∠ A = α = 138.4110608231° = 138°24'38″ = 2.41657208333 rad
Angle ∠ B = β = 36.5° = 36°30' = 0.6377045177 rad
Angle ∠ C = γ = 5.0899391769° = 5°5'22″ = 0.08988266433 rad

Height: ha = 3.06604908523
Height: hb = 3.41553303714
Height: hc = 22.90106772899

Median: ma = 15.42107365693
Median: mb = 21.37328593394
Median: mc = 36.46441151247

Inradius: r = 1.50878197495
Circumradius: R = 299.0002339927

Vertex coordinates: A[5.14552145419; 0] B[0; 0] C[30.94884891338; 22.90106772899]
Centroid: CG[12.03112345586; 7.63435590966]
Coordinates of the circumscribed circle: U[2.5732607271; 28.88659007729]
Coordinates of the inscribed circle: I[4.5732607271; 1.50878197495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 41.5899391769° = 41°35'22″ = 2.41657208333 rad
∠ B' = β' = 143.5° = 143°30' = 0.6377045177 rad
∠ C' = γ' = 174.9110608231° = 174°54'38″ = 0.08988266433 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b we calculate side c - by using the law of cosines and quadratic equation:  Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines   ### 10. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 38.5   b = 34.5   c = 56.75217637256

Area: T = 649.8276913357
Perimeter: p = 129.7521763726
Semiperimeter: s = 64.87658818628

Angle ∠ A = α = 41.5899391769° = 41°35'22″ = 0.72658718203 rad
Angle ∠ B = β = 36.5° = 36°30' = 0.6377045177 rad
Angle ∠ C = γ = 101.9110608231° = 101°54'38″ = 1.77986756563 rad

Height: ha = 33.75772422523
Height: hb = 37.6711125412
Height: hc = 22.90106772899

Median: ma = 42.83662445014
Median: mb = 45.32204572239
Median: mc = 23.04547245266

Inradius: r = 10.01664636641
Circumradius: R = 299.0002339927

Vertex coordinates: A[56.75217637256; 0] B[0; 0] C[30.94884891338; 22.90106772899]
Centroid: CG[29.23334176198; 7.63435590966]
Coordinates of the circumscribed circle: U[28.37658818628; -5.9855223483]
Coordinates of the inscribed circle: I[30.37658818628; 10.01664636641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4110608231° = 138°24'38″ = 0.72658718203 rad
∠ B' = β' = 143.5° = 143°30' = 0.6377045177 rad
∠ C' = γ' = 78.0899391769° = 78°5'22″ = 1.77986756563 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b we calculate side c - by using the law of cosines and quadratic equation:  Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    